Bizarro-world math: Ornaments that defy geometry

Fancy some Christmas ornaments that defy conventional Euclidean geometry? In these animations, created by mathematician and artist Jos Leys, you can see what Christmas ball patterns would look like in hyperbolic space, a "bizarro world" where parallel lines can intersect and the three angles of a triangle add up to less than 180 degrees.

The different ornament designs show various ways that 2D hyperbolic space can be tiled with polyhedron shapes by varying the Poincaré disc model. Developed by Henri Poincaré of Poincaré conjecture fame these tesselations have also been explored by artist MC Escher in a series of prints.

I am afraid I have to quit using New Scientist.
Reason... I have to download the exact same add every time i want to watch a video. even when they are all on the same page.
In some countries we pay per MB for internet.
Sorry N/S but I can not afford your free subscription.

Tom Barringer
on December 25, 2011 1:53 AM

What are the fractal properties of these images?

Robert
on December 25, 2011 3:13 AM

Yes, the unbearable repeating commercials are the main reason why I rarely watch the New Scientist videos. This is a problem of most of the webpages though: inundation with ads and commercials. Pure madness! Soon there won't be any real content left to read/watch, just the damned commercials (see any TV channel for reference).

I really don't care what I would do "If I could power a city". Maybe the energy lost on replaying this commercial can power a city...